Math intro courses guide

1. This year’s calculus placement exam will be open from 9am on July 1 to 12pm (noon) on July 31. In general, opening dates of all placement exams are listed on the following Yale College site.  Details about the math placement test can be found below. 

2. Individual “walk-in” calculus placement advising sessions will take place via zoom at the beginning of August.  The schedule will be posted here. 

If you need placement advice, wait to submit your preference selection entry until after the advising session (you will have several more days to submit, and the timing of your entry does not affect the lottery outcome in any way). 

Please note that to receive advice, you must first complete the placement exam - advisers cannot give you placement without it.

3. There will also be a Math 2250 / Math major town hall  run via zoom in early August. It will be led by the instructor of Math 2250) and Miki Havlickova (a director of undergraduate studies in math). We will have a short presentation at the beginning, and then stay for questions.

4. Preference selection for sections of calculus (Math 110, 112, 115, 116, 120) will be open during university-set times at the beginning of August . Please note that the timing of your entry is not taken into account in any way. In particular, you will not be disadvantaged if you submit your entry after the advising sessions. (You may not enter preference selection for two different levels of calculus, so it is important to settle on your placement in advance.)

5. The academic fair will take place during orientation as scheduled by the University. The Fair is a great place to ask questions about the mathematics major, courses at the 2000 level or higher, mathematics community, etc. (Please note that advisers at the Fair cannot help with calculus placement - for placement advice at the 1000 level, please attend one of the sessions listed above.) 

Detailed general information about the Fair can be found on the Yale Academic fair website. 

• For detailed information about the test, visit our Calculus and placement exam FAQ. The test is typically open in July. 
• All incoming students who wish to take calculus during their first two years at Yale should take the test during the summer, so that they can have the results available, and take advantage of August advising. This includes students who have taken AP Calculus - your scores will be taken into account, but you will still have to complete the exam. 
• The test is not required for registration in math courses level 2000+. If you wish to start in Math 225, for example, you can just register for it.  For information about starting in level 2000 courses, please be sure to read the section on “choosing your first math course(s)” below.
• The exam is available through Canvas, on a site called “Math placement exam [current year]”. The link to Canvas is https://canvas.yale.edu/ . All incoming first-year students are automatically enrolled on the site at the end of June. Rising sophomores, juniors, and seniors should contact math.dus@yale.edu to be added to the site. 
• Results of the test are available within five minutes from submission. You can access them by clicking on the “placement results” tab. (If the tab does not load, try a different browser - Canvas does not interact well with certain browsers. If that does not help, please send a message to canvas@yale.edu for technical support, and cc math.dus@yale.edu .) 
• If you would like to take a course that differs from your placement exam result, please attend our calculus advising session in August. The advisers will be happy to help you. Note that you must take the test first - advisers cannot give you placement without it. Detailed information about the session will be posted on this site by the middle of July. 
• After receiving placement to take your first calculus course, pre-register for the class through Yale’s preference selection website. Preference selection is typically open in August (for the Fall term), and in December (for the Spring term). 
• Results of the test are valid for two years, and students may not take the exam again within this period. If you wish to discuss the possibility of changing your placement, please attend one of our placement advising sessions.
• Please note that students who previously enrolled in a calculus course at Yale are ineligible to take the placement exam, whether they completed the course or not. If you are in this situation and wish to consider a change of placement, please consult the DUS Miki Havlickova at math.dus@yale.edu. 

First you should complete the placement exam - our advisers can only assist with your placement after that. 

Once you have completed the exam, if it is June, July, or early August: Please plan to attend our zoom placement advising session, listed in the event schedule above.  This is the main event of the year, and we strongly encourage you to attend, as it is the best place to get placement advice. The event takes place before the end of August preference selection, so it will be in time for you to register for Fall (or Spring) calculus sections. 

Outside of the main session, our individual advising resouces are limited. We will likely have a smaller advising session at the end of August; if so, it will be announced in the event schedule above. 

 During the rest of the year, please reach out to the course director of the course that you would like to take, to discuss your placement. (If you’re not sure which course, then you can just pick any of the course directors.)  The list of course directors is on the bottom of this page.

Please note that the course directors have a lot to manage, particularly at the beginning of the year, and it’s unlikely that they will instantly be able to schedule an appointment with everyone who reaches out to them for individual advice about placement - we have over a thousand students in calculus every year! We encourage you to take the placement exam early in the summer, and attend the main August advising session, if at all possible, so that you’re sure to get the advice you need in a timely manner. 

• Take the placement exam on Canvas. (You must do this even if you have AP scores.)
• If you have questions about the calculus courses or placement exam, check the calculus and placement exam FAQ.
• If you have questions about your placement, attend our calculus advising session in August. Schedule of the sessions will be posted on top of this site by the middle of July. 
• If you need help with your placement and missed the advising session, write to the faculty member listed below as a contact for the course into which you were placed. 
• Pre-register for your first calculus course via Preference selection, typically during the second week of August. Note that you must have placement in the course in order to enroll, and you may not enter preference selection for more than one calculus course at the same time.
• If you miss preference selection, or need to switch section after it runs, you will be able to do so once registration opens at the beginning of term. You can sign up for any section of the course where you have placement, if the section has open spots. 

• Read the “choosing your first math course(s)” section below for advice about where to get started. If you have questions about anything, you can stop by the Academic Fair at the end of August, visit our August DUS office hours (listed on the Math DUS site), or write to math.dus@yale.edu . 
• If you choose to start in a course level 2000+ (such as Math 2250), you do NOT need to take the calculus placement exam. If you have the pre-requisites for your chosen course, you can simply sign up once registration opens.
• If you have already completed multivariable calculus, linear algebra, or other advanced math courses, the notes in “choosing your first math course(s)” will help guide you through the options. (This is especially important if your potential major(s) require math, as you will need to make arrangements about the requirements with the major’s DUS right away.) 

Please see the section below on “Choosing your first math course” at Yale. It is sorted by major, and has recommendations for what courses may be good to start with, as well as detailed notes about procedures to follow if you have already completed some of them. 

Math 1120 focuses on differential calculus, where the goal is to measure a function’s instantaneous rate of change (the derivative). First, we define limits, which allow us to talk rigorously about instantaneous changes. Then, we define the derivative and find many rules that simplify its computation. Next, we apply the derivative to better understand function behavior (allowing us to minimize cost or maximize profit in economic models). Finally, we develop strategies for reversing the derivative process to find antiderivative functions. These antiderivatives have surprising applications, like computing areas and modeling population growth.

Math 1120 requires the placement exam. Students typically take the course after completing pre-calculus.  

Another option is the Math 1100/1110 sequence, a two-semester course that integrates pre-calculus and differential calculus topics. Successful completion of Math 1100 and 1110 is equivalent to Math 1120 in that it satisfies the same major and professional-school (e.g. pre-med) requirements; however a student completing Math 1100 and 1110 receives two course credits and two QR credits.  

Math 110/111 requires the placement exam. Some prior knowledge of pre-calculus is helpful. 

Math 1150 investigates the mathematics of accumulation. With integral calculus, we use information about instantaneous rates (like the velocity of a moving object) to compute net changes (like change in position). Series convergence tests and Taylor series help us understand how calculators work, and various other topics (solids of revolution, parametric equations, polar coordinates) allow us to apply the tools of single variable calculus in broader contexts. Throughout the semester, we consider both exact and approximate solutions to problems and investigate the role of error.

Math 1150 and 1160 both cover integral calculus, and both can be used as pre-requisites for any course that requires Math 1150. Math 1160 places emphasis on applications to biology, and is particularly suitable for biology and pre-medical students.

Math 1150 and 1160 require the placement exam, or completion of Math 111 or 112 at Yale. Typically, students place into Math 1150 after completing a differential calculus course such as AP Calculus AB. 

Math 1200 extends skills and knowledge you gain in single variable calculus to two and three variables. We will study how to graph surfaces and solids in three dimensions, differentiate and integrate functions of several variables, optimize functions of several variables (for example when maximizing profit in economics),  we will learn how to integrate along curves and surfaces (for example when calculating how much energy a solar panel will generate while the sun is shining on it), and many other topics.

Math 1200 and 1210 both cover multivariable calculus, and both can be used as pre-requisites for any course that requires Math 1200. Math 1210 places emphasis on applications to biology, and is particularly suitable for biology and pre-medical students. [Note that Math 1210 is typically only offered every other year.]

Math 1200 and 1210 require the placement exam or completion of Math 1150 or 1160 at Yale. Typically, students place into Math 1200 after completing an integral calculus course, such as AP Calculus BC. 

Math 2250 is a linear algebra course, and a part of our introductory sequence into the math major. In linear algebra, you will learn key language and concepts used throughout pure mathematics as well as in a wide variety of applications.  Linear algebra starts by studying systems of equations with many variables, and it builds a detailed understanding of how to work in abstract n-dimensional space. This version of linear algebra focuses on concepts, and provides an introduction to writing mathematical proofs.

Math 2250 usually has a zoom town hall meeting in early August: it will be listed under the “Summer / Fall event schedule” toward the top of this page. 

We also offer an intensive version of this course, Math 2260, for students who are looking for an extra challenge. Math 226 will teach the same main topics as Math 2250, but it may go into more depth, ask more challenging problems on homework and exams, or cover optional side topics. Both courses prepare students equally well for subsequent mathematics courses, or for using proofs, problem solving skills, and linear algebra in other fields. 

If you start in Math 2260, and find that it is too time consuming, you can move to Math 2250 until Midterm. You can read more about how moving between courses work in our Calculus FAQ. 

Math 2220 is a linear algebra course best suited for students who wish to focus on applications and practical solving problem practice, rather than abstract mathematics and mathematical proofs. It is often taken by students majoring in engineering, technology, science, social sciences, and economics. Mathematics majors, as well as students majoring in Math + CPSC or Math + Econ, need to complete Math 2250 or 2260, and may not enroll in Math 2220. 

Math 2220, 2250, and 2260 do not require the placement exam or preference selection, you can simply sign up for them when registration opens. They can be taken directly after integral calculus, though most students complete multivariable calculus first. For advice about whether linear algebra may be the best place for you to start, please see the section below on choosing your first math course(s) at Yale (particularly if you have not yet taken multivariable calculus, and it may be required by your prospective major or other courses you plan to take). 

Math 2550 is an introduction to real analysis, and a part of our introductory sequence into the math major. The topics are similar to differential and integral calculus, but it’s done in a rigorous way that focuses on proofs and details of the concepts that happen behind the scenes in calculus.  Said differently, our calculus sequence teaches you how to use the tools of limits, derivatives, and integrals to solve a variety of problems, whereas this course teaches you how to build all of those tools from scratch.

We also offer an intensive version of this course, Math 2560, for students who are looking for an extra challenge. Math 2560 will teach the same main topics as Math 2550, but it may go into more depth, ask more challenging problems on homework and exams, or cover some optional side topics. Both courses prepare student equally well for subsequent math courses, or for using real analysis in other fields. 

Math 2550 and 2560 require prior completion of Math 2250 or 2260.

Math 2550 and 2560 do not use the placement exam or preference selection. It requires Math 2250 or 2260. If you have taken a proof-based linear algebra course elsewhere, and are considering Math 2550 or 2560 as your first math course, please contact the Math DUS at math.dus@yale.edu to assist you with placement, as well as with requirements of your potential major (if it requires linear algebra). For more information, see section on choosing your first math course(s) below. 

Math 3020 is a rigorous and exciting course that explores some of the beautiful connections between linear algebra and real analysis. For this reason, it requires completion of 2250/2260 and 2550/2560. 

This course is an introduction to manifolds, which are low-dimensional shapes living in a higher dimensional universe (e.g., a one-dimensional coat hanger or a two-dimensional eggshell each living in a three-dimensional world), and it teaches how to do calculus in this abstract setting.  Although the focus of this course will be on abstract mathematical objects and their properties, the material in this course also has applications to a broad range of topics including theoretical physics and machine learning.

Many students who have not completed multivariable calculus in high school would benefit from taking Math 120. However, prospective math majors, and students excited about rigorous proof-based math should consider taking Math 2250/2260, Math 2550/2560 and Math 3020 instead.  Math 3020 is also appropriate for students who have already completed Math 1200 and are curious to learn multivariable analysis rigorously. (Note that Math 3020 can only be taken after Math 2250 and 2550.) 

Math 3020 does not use the placement exam or preference selection. It requires both proof-based linear algebra, and real analysis (Math 2250 and 2550). If you have taken similar courses elsewhere and wish to start at Yale with Math 3020, please be sure to contact the Math DUS during the summer before your first year, at math.dus@yale.edu , so we can help you as far as course placement as well as requirements of your potential major. For more information, please see the section on choosing your first math course(s) below. 

Math 1180 teaches a combination of multivariable calculus and linear algebra. It is suited for students majoring in Economics or Social sciences who wish to learn the most relevant mathematics in one semester.  Students intending to take further courses in mathematics, or wishing to go to graduate school in their field, should consider multivariable calculus (Math 1200) and linear algebra (Math 2220, 2250, or 2260) instead. 

Pre-requisite for Math 1180 is differential calculus (such as Math 1120 or AP Calculus AB). Knowledge of integral calculus is recommended. 

The math department offers other Quantitative Reasoning (QR) courses that assume no calculus experience:

In Math 1070 (Mathematics in the real world), students use mathematical ideas to solve real world problems. Topics include compound interest, population growth, probability and its applications to games of chance, mortgage payments, false positives in drug testing, computer security, and other questions. 

Math 1080 (Estimation and error) leads students through a problem-based investigation of basic mathematical principles and techniques that help make sense of the world. Applications include geology, ecology, finance, and other fields. 

Math 2410 and 2420: probability and statistics teach us how to collect, analyze, and interpret data. That being so, it is directly useful in almost any field where experiments, surveys, or other means for data collection are employed.

Math 2440: discrete mathematics includes many topics of interest in computer science.

Math 2460: differential equations can be used for modeling complex systems in biology, physics, economics, and other fields. 

Math 2700: set theory is at the foundation of mathematics and often taken by philosophy students.

Many incoming students enroll in one of our calculus courses (Math 1100, 1120, 1150, 1160, 1200, or 1210). Within calculus, the sequence of courses is

1. Math 1100 + 1110 or Math 1120 (differential calculus, similar to AP Calculus AB)
2. Math 1150 or Math 1160 (integral calculus, similar to AP Calculus BC)
3. Math 1200 or Math 1210 (multivariable calculus). [Note that Math 1210 is only offered every other year.]

If you are considering taking calculus, you will need to complete our placement exam, so that we can help you determine the best place to start. We highly recommend taking the test during the summer before you first enroll at Yale. The result will be valid for two years.

Pre-requisite for the mathematics major is integral calculus (for example Math 1150, or AP Calculus BC). 

Following the pre-requisite, the introductory sequence includes:

• Linear algebra (Math 2250 or 2260),
• Real analysis (Math 2550 or 2560),
• Multivariable analysis or calculus (Math 3020 or 1200). Note that Math 3020 can only be taken after Math 2250 and 2550.

Most students complete multivariable calculus before enrolling in linear algebra. 

Prospective mathematics majors and students with interest in abstract mathematics may consider enrolling in Math 2250 (or 2260) directly after integral calculus (e.g. Math 1150 or AP Caclulus BC), and completing their vector analysis/multivariable calculus requirement with Math 3020 (after finishing 2250 and 2550). 

The placement exam is NOT required for any math course level 2000 or above. In particular, you do not need it in order to enroll in Math 2250, or 2260. For information about starting in level 2000 courses, please be sure to read the section on “choosing your first math course(s)” below. 

If you have not completed a full integral calculus course, including sequences and series, then you will need to complete the calculus placement exam, and start in the calculus sequence. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed integral calculus but have not done multivariable calculus, then the best course to start with is either Math 1200, or Math 2250 or 2260. Note that Math 1200 requires the placement exam; Math 2250 and 2260 do not. 

Most students with integral calculus background will start with Math 1200, to finish the calculus sequence, and gain more experience with mathematics before enrolling in proof-based courses. This choice is recommended particularly if you may need multivariable calculus for another major you are considering, or if it is needed for other courses you might like to take soon (such as in physics or economics). After Math 1200, you would move to Math 2250 or 2260, and Math 2550 or 2560, which would complete your introductory sequence requirement.

If you are excited to start with proof-based mathematics right away, then Math 2250 or 2260 may be the best course. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 2550 or 2560, and you would afterward complete the introductory sequence with Math 3020 (or with Math 1200, if you decide later that you prefer that). 

If you have completed multivariable calculus but have not taken linear algebra, then the best choice is Math 2250 or 2260. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 2550 or 2560, and you would afterward complete the introductory sequence with Math 3020. None of these courses require a placement exam. 

(You will not need to have your multivariable calculus course evaluated by the math department, since it would not change the requirements in any way: all students have the option of satisfying the multivariable requirement with Math 3020, whether or not they have already completed a course equivalent to Math 1200. Note that Math 3020 can only be taken after Math 2250 and 2550.) 

If you have completed multivariable calculus and have taken linear algebra, then the options are as follows:

First, we need to determine whether your linear algebra course was a theoretical, fully proof-based course intended for mathematics majors, or not. Most linear algebra courses are not, and then you will still need to enroll in Math 2250 or 2260. 

A proof-based course teaches techniques for writing mathematical proofs, and problem sets and exams focus mostly on proving abstract mathematics results. If the course explicitly taught students how to prove results (such as by induction and by contradiction), and nearly every assigned problem had the phrase “prove [something]” in it, then the course was probably proof based; if not, then it probably wasn’t. 

If you are not sure whether your linear algebra was proof-based or not, send a syllabus and either an exam or a problem set (the questions, not the solutions) to math.dus@yale.edu; we will be happy to take a look and advise you.

If the linear algebra course was not proof based, then you will still need to take Math 2250 or 2260. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 2550 or 2560, and you would afterward complete the introductory sequence with Math 3020.

If the linear algebra course was proof based, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 2250, we will give you permission to substitute Math 3400 for Math 2250, in requirements of the math major. We will also help you find the best starting course (likely Math 2550 or 2560 – or higher, if you have taken real analysis as well). Please note that this permission has to be granted by the Math DUS - obtaining permission from the Math 2550 instructor to enroll will not take care of requirements of the math major. 

To evaluate the course, we will need a copy of the syllabus or another document with a detailed list of topics taught, a copy of your transcript (unofficial is fine), and a final exam for the course. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu . 

If your course is not evaluated as equivalent to Math 2250, you can try placing out of Math 2250 by taking an exam during the summer before your first semester at Yale. Please reach out to math.dus@yale.edu before mid-August, and we will help you with the arrangements. 

The exam takes place at the end of August, after everyone is on campus, usually the Tuesday before classes start. It is around 90 minutes long, and it is focused on proof writing, and the theoretical side of linear algebra (same way as Math 2250). 

Note that the test must be taken before you first enroll at Yale, and that it does not grant course credit – it may only allow you to substitute Math 3400 for Math 2250.

To sign up for the exam, you must e-mail math.dus@yale.edu by August 15. 

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 120. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed a multivariable calculus course equivalent to Math 1200, then please reach out to the math DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but this does not mean you have to repeat content you already know.

One option is to request DUS permission to substitute Math 3020 (multivariable analysis). (Note that Math 3020 can only be taken after Math 2250 and 2550.) You must have this permission in writing, obtained in advance of this substitution - please reach out to the DUS as soon as possible. For this permission, we will only need a copy of your transcript (unofficial is fine) that shows completion of the class.

If you would like to obtain permission to substitute other classes in the same area, such as Math 2460, we can evaluate the course you have taken, to see if it is reasonably equivalent to Math 1200. For the evaluation, we will need a copy of the syllabus or another document with a detailed list of topics taught, a copy of your transcript (unofficial is fine), and a final exam for the course. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu . When you send the materials, please be sure to mention that the evaluation is for the CPSC + Math major. 

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 2250 or 2260 (proof-based linear algebra), and Math 2440 (discrete math). We strongly recommend taking Math 2250 or 2260 before Math 2440, as the former provides a thorough preparation in proof writing, and this is very helpful skill in Math 2440.

If you have already taken some of these courses prior to enrolling at Yale, please reach out to the DUS at math.dus@yale.edu as soon as possible. We will work with you to evaluate the courses, and find the best possible options for you as far as requirements of the major. 

Other courses frequently taken by Math + CPSC majors include Math 2410 (probability theory), Math 2460 (ordinary differential equations), Math 2550 (analysis 1), Math 2700 (set theory), Math 3050 (analysis 2), Math 3500 (abstract algebra). You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 1200. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

For Math + Econ majors, it is important to take multivariable calculus as soon as possible. We recommend starting with your Yale calculus classes right away, in the Fall of your first year.

If you have completed a multivariable calculus course equivalent to Math 1200, then please reach out to the math DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but this does not mean you have to repeat content you already know.

One option is to request DUS permission to substitute Math 3020 (multivariable analysis). (Note that Math 3020 can only be taken after Math 2250 and 2550.) You must have this permission in writing, obtained in advance of this substitution - please reach out to the DUS as soon as possible. For this permission, we will only need a copy of your transcript (unofficial is fine) that shows completion of the class.

If you would like to obtain permission to substitute other classes in the same area, such as Math 2460, we can evaluate the course you have taken, to see if it is reasonably equivalent to Math 1200. For the evaluation, we will need a copy of the syllabus or another document with a detailed list of topics taught, a copy of your transcript (unofficial is fine), and a final exam for the course. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu . When you send the materials, please be sure to mention that the evaluation is for the Econ + Math major. 

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 2250 or 2260, and Math 2550. Math 2250 or 2260 must be taken first.

If you have already taken some of these courses prior to enrolling at Yale, please reach out to the DUS at math.dus@yale.edu as soon as possible. We will work with you to evaluate the courses, and find the best possible options for you as far as requirements of the major. 

Other courses frequently taken by Math + Econ majors include Math 2440 (discrete math), Math 2460 (differential equations), Math 2700 (set theory), Math 3300 (advanced probability). You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 1200. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed a multivariable calculus course equivalent to Math 1200, then please reach out to the math DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but this does not mean you have to repeat content you already know.

One option is to request DUS permission to substitute Math 3020 (multivariable analysis). (Note that Math 3020 can only be taken after Math 2250 and 2550.) You must have this permission in writing, obtained in advance of this substitution - please reach out to the DUS as soon as possible. For this permission, we will only need a copy of your transcript (unofficial is fine) that shows completion of the class.

If you would like to obtain permission to substitute other classes in the same area, such as Math 2460, we can evaluate the course you have taken, to see if it is reasonably equivalent to Math 1200. For the evaluation, we will need a copy of the syllabus or another document with a detailed list of topics taught, a copy of your transcript (unofficial is fine), and a final exam for the course. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu . When you send the materials, please be sure to mention that the evaluation is for the Math + Phil major. 

While linear algebra is not required for the major, we very much recommend completing Math 2250 or 2260, partly for the topic they teach, and partly because they provide a thorough preparation with proof writing, which is an essential skill for the major.

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 2700. We recommend first completing Math 2250 or 2260, for the extra proof preparation, but this is not required. 

Other courses frequently taken by Math + Phil majors include Math 2410 (probability theory), Math 2440 (discrete math), Math 2460 (differntial equations), Math 2550 (analysis 1).   You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 1200. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

For Math + Phys majors, it is important to take multivariable calculus as soon as possible. We recommend starting with your Yale calculus classes right away, in the Fall of your first year.

If you have completed a multivariable calculus course equivalent to Math 1200, then please reach out to the math DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but this does not mean you have to repeat content you already know.

One option is to request DUS permission to substitute Math 3020 (multivariable analysis). (Note that Math 3020 can only be taken after Math 2250 and 2550.) You must have this permission in writing, obtained in advance of this substitution - please reach out to the DUS as soon as possible. For this permission, we will only need a copy of your transcript (unofficial is fine) that shows completion of the class.

If you would like to obtain permission to substitute other classes in the same area, such as Math 2460, we can evaluate the course you have taken, to see if it is reasonably equivalent to Math 1200. For the evaluation, we will need a copy of the syllabus or another document with a detailed list of topics taught, a copy of your transcript (unofficial is fine), and a final exam for the course. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu . When you send the materials, please be sure to mention that the evaluation is for the Math + Phys major. 

While linear algebra is not required for the major, we very much recommend completing Math 2220, 2250 or 2260, as it teaches skills directly relevant to the major, as well as to many of the potential subsequent courses. For students who wish to keep open the possibility of taking proof-based courses in the future, Math 2250 or 2260 is highly recommended over Math 2220, as the former provides a thorough preparation with proof writing.

Other courses frequently taken by Math + Phys majors include Math 2410 (probability theory), Math 2440 (discrete math), Math 2460 (differntial equations), Math 2550 (analysis 1). Students interested in theoretical physics and proof-based courses often include some of the level 3000 courses, most often Math 3050 (analysis 2), Math 3100 (complex analysis), or Math 3500 (abstract algebra). You can find more information about most of these courses in the above section on “Math introductory courses”.

For majors other than the mathematics ones listed above, we share below some notes that may help you get started. We would also encourage you to speak with your (intended) major’s DUS - they are the best person to advise you about courses to take. 

If you have completed some of your major’s requied math courses prior to enrolling at Yale, please reach out to the major’s DUS for advice, and to ask what options may be available as far as completing the requirements. (The math DUSes are happy to provide advice, but any arrangements about requirements of another major must be settled with the major’s DUS, rather than with the Math department.)

Now the notes:

Most Yale students complete a calculus course at some point during their studies. If you have not yet completed the calculus sequence all the way through multivariable, and you either wish to continue with the sequence, or you want to keep your options open as far majors or other courses that require calculus, then one of the courses in the calculus sequence may be a great place to start.

In order to enroll, you will need to complete the placement exam, and then register for a section of your course through preference selection. For details, see the above notes about the calculus sequence, placement exam, and checklist for enrolling in calculus.

If you have never taken calculus, do not expect to need calculus for your major or other classes, and would prefer to take another kind of math course at Yale, then you might enjoy one of our level 1000 seminars (numbered 1010 - 1099): these are described above under “Other courses at the 1000 level”. The seminars have limited enrollment, and do not expect any prior knowledge of calculus. They teach a combination of math topics and problem solving skills that can be useful for students in any major.

If you have completed a multivariable calculus course, and your major does not require calculus, then you can enroll directly in a higher level math course. You do not need to have your previous math courses evaluated: for purposes of pre-requisite to other courses, you can simply tell the instructor that you have completed the relevant course prior to enrolling at Yale. 

For courses to start with, after multivariable: Frequent choices for many majors include linear algebra (Math 2220, 2250, or 2260), probability theory (Math 2410), discrete mathematics (Math 2440), or differential equations (Math 2460). You will find these described under “Linear algebra” and “Other courses at the 2000 level” above. If you need any help choosing, please don’t hesitate to stop by the academic fair, write to math.dus@yale.edu, stop by one of our August office hours (to be posted on the Math DUS website,) or consult the DUS of your major for recommendations.

If you have completed a multivariable calculus course and your major does require calculus, then you will need to meet with the DUS of your major to discuss what the options may be. Some majors allow students to substitute a higher level math course, for example. You will not need to have the course evaluated by the Math department: options regarding the requirements must be done with the DUS of the major. We are happy to help you decide which math course to start with, however, so please feel free to stop by or write to math.dus@yale.edu for advice. 

With additional questions, a good place to start are our FAQ’s:

• Placement exam and calculus FAQ,  
• Math major and advanced courses FAQ

If your question is not addressed there, please contact the Math DUS at math.dus@yale.edu .  Please allow at least two weekdays for an answer. (During school recess, especially winter and summer break, our response time may be longer.) 

For questions about the calculus courses, please contact the course director listed below. For single-section courses, the best person to contact is the instructor. 

• For questions about calculus placement: Please attend the zoom calculus advising session in early August (listed in the schedule toward the top of this page). 
• Math 1100 and 1110: Sarah Days-Merrill
• Math 1120: Meghan Anderson (Fall), Maria Siskaki (Spring)
• Math 1150: Brett Smith (Fall), Bailey Heath (Spring)
• Math 1200: John Hall (Fall and Spring)
• For questions about a specific single-section course, the best person to ask is the instructor (listed in Yale Course Search). 
• For other advice (e.g. about level 2000+ course selection or requirements of the major), please don’t hesitate to reach out to math.dus@yale.edu

The Student Accessibility Services (SAS) Office works with students with ADHD/Autism/learning difficulties, sensory or motor disabilities, mental health concerns, temporary disabilities like concussions and serious injuries, and more. Our peer liaison program is designed so that first-years can connect with someone who has first-hand experience with navigating accommodations at Yale. If you think you could benefit from additional resources in regards to academics and general college life, please don’t hesitate to fill out this form and the PL for your college will reach out ASAP.